Isotherms Henry’s law

The ideal gas law equation of state thus leads to a linear or Henry s law isotherm. A natural modification adds a co-area term ... 

Equation (5.22), which is referred to as Henry s law isotherm, predicts a linear relationship between T2 and C2. 

The concentration of molecules dissolved by the ordinary dissolution process, c, is related to the penetrant equilibrium pressure, p, by a Henry s law isotherm ... 

Figure 1. Conventional plot of sorption of water by poly(ethyl methacrylate) top curve, experimental data from Ref. 5. Bottom curve, calculated Henry s Law isotherm based on extension of low relative pressure sorption...

At any relative pressure, the experimental sorption can be compared to that predicted for the Henry s Law Isotherm to provide a ratio, N, which will be termed the "enhancement number", calculated from Equations (1) and (2) as follows ... 

A low ( 1, A = Ao) or high (1 - 1, A — Amin) coverages, however, the variation in RT In 6/(1 - 6) becomes predominant then the adsorption isotherm becomes practically Langmuirian (at very low or 1 - 6—Henry s law isotherm), and the kinetic relations become similar to those described at the very beginning of this chapter. 

Simple addition of the true activation energy and the heat of adsorption takes place only in the case of the Henry s law isotherm with other isotherms, the picture becomes more complicated and must be analyzed separately in each specific instance. 

Applications of Hobson s Method.—Zeldowich s kernel approximation [equation (6)] discussed in Section 2 has been generalized by Hobson to account for adsorbate lateral interactions. The major problem associated with the Langmuir equation is its inability to predict phase transitions. Rather than use the step approximation to the local isotherm, Hobson chooses a combination of a Henry s law isotherm and a step approximation , as shown in Figure 1(c) ... 

General.—Adsorption from dilute solutions can, in the limit of sufficiently low concentrations, be described by a linear (Henry s law) isotherm, which may, however, be expressed in various forms. Among the possible definitions are the... 

Figures Transition from Henry s law isotherm in range 0— c to Dubinin-...

Examples of the matches are shown in Figs. 84-86. In these figures the dotted line is the second derivative of the DP equations and the circles are the overall DP isotherm. The solid lines are the results expected from the X theory with a distribution for both the and pore size. Fig. 84 shows the DP isotherm which is identical to Henry s law isotherm, = 1, whereas Fig. 85 shows a more realistic Freundlich isotherm with Vp = 0.5. The only difference is a shift on the x axis. 

Fig. 84. Comparison of Henry s law isotherm to a x theory plot with an distribution and a pore distribution.

When the Murphree efficiency is constant for all trays, and under conditions such that the operating line and equilibrium curves are straight (Henry s law, isothermal operation, dilute solutions), the overall tray efficiency can be computed and the number of real trays can be determined analytically ... 

Figure 6.2 Graphical solution to the single-stage contacting example (a) Henry s law isotherm with an adsorbent intitiaily free from the adsorbate (b) Henry s law isotherm with an adsorbent initially having an adsorbate loading of qo and (c) general Type I isotherm with an adsorbent initially free from the adsorbate.

For a multistage process involving N stages the general result for a linear (Henry s law) isotherm is ... 

Make a plot of Eq. XVII-69 as 6 versus P, and, for comparison, one of a Langmuir adsorption isotherm of same limiting or Henry s law slope. Comment on the comparison. 

The results of a comparison between values of n estimated by the DRK and BET methods present a con. used picture. In a number of investigations linear DRK plots have been obtained over restricted ranges of the isotherm, and in some cases reasonable agreement has been reported between the DRK and BET values. Kiselev and his co-workers have pointed out, however, that since the DR and the DRK equations do not reduce to Henry s Law n = const x p) as n - 0, they are not readily susceptible of statistical-thermodynamic treatment. Moreover, it is not easy to see how exactly the same form of equation can apply to two quite diverse processes involving entirely diiferent mechanisms. We are obliged to conclude that the significance of the DRK plot is obscure, and its validity for surface area estimation very doubtful. 

Henry s law corresponds physically to the situation in which the adsorbed phase is so dilute that there is neither competition for surface sites nor any significant interaction between adsorbed molecules. At higher concentrations both of these effects become important and the form of the isotherm becomes more complex. The isotherms have been classified into five different types (9) (Eig. 4). Isotherms for a microporous adsorbent are generally of type I the more complex forms are associated with multilayer adsorption and capillary condensation. 

Equation 6 shows that the adsorption of component 1 at a partial pressureis reduced in the presence of component 2 as a result of competition for the available surface sites. There ate only a few systems for which this expression (with 5 1 = q 2 = 5 ) provides an accurate quantitative representation, but it provides useful quaUtative or semiquantitative guidance for many systems. In particular, it has the correct asymptotic behavior and provides expHcit recognition of the effect of competitive adsorption. For example, if component 2 is either strongly adsorbed or present at much higher concentration than component 1, the isotherm for component 1 is reduced to a simple linear form in which the apparent Henry s law constant depends onp. ... 

Thermodynamics requires that a linear limit be approached in the Henry s law region for all isotherm equations. 

This three-parameter equation behaves linearly in the Henry s law region and reduces to the Langmuir isotherm for m = 1. Other well-known isotherms include the Radke-Prausnitz isotherm [Radke and Prausnitz, Ind. Eng. Chem. Fundam., 11, 445 (1972) AIChE J., 18, 761 (1972)]... 

The simplest mode of IGC is the infinite dilution mode , effected when the adsorbing species is present at very low concentration in a non-adsorbing carrier gas. Under such conditions, the adsorption may be assumed to be sub-monolayer, and if one assumes in addition that the surface is energetically homogeneous with respect to the adsorption (often an acceptable assumption for dispersion-force-only adsorbates), the isotherm will be linear (Henry s Law), i.e. the amount adsorbed will be linearly dependent on the partial saturation of the gas. The proportionality factor is the adsorption equilibrium constant, which is the ratio of the volume of gas adsorbed per unit area of solid to its relative saturation in the carrier. The quantity measured experimentally is the relative retention volume, Vn, for a gas sample injected into the column. It is the volume of carrier gas required to completely elute the sample, relative to the amount required to elute a non-adsorbing probe, i.e. 

The stripping operation takes place isothermally at 298 K and follows Henry s law. 

With the adsorbate concentration low enough, the Langmuir isotherm transforms into the linear equation and becomes the simplest isotherm of adsorption, as described by Henry s law. 

The adsorption free energy and other parameters may be determined, provided that a proper adsorption isotherm is identified and is fitted to experimental data. However, it is usually difficult to unequivocally choose an appropriate isotherm an experimental isotherm may well be fitted to a multitude of theoretical isotherms having several adjustable parameters. If the adsorption isotherm at a very small surface coverage is accessible experimentally, the adsorption free energy can be determined from the limiting slope of the isotherm, as all isotherms reduce to Henry s law when 6 0 ... 

The simplest adsorption isotherm is that of Henry s law (linear adsorption isotherm),... 

In other words, the model predicts a limiting form of a linear (Henry s Law) type of isotherm as the polymer concentration tends to zero. 

---